Noncommutative Brownian motion

TL;DR

This paper explores how noncommutative geometry affects classical Brownian motion, revealing a unique correlation signature that could help experimentally detect spatial noncommutativity.

Contribution

It introduces a formalism for analyzing Brownian motion in noncommutative space and identifies observable effects of noncommutativity on particle correlations.

Findings

Noncommutativity induces non-zero correlations between coordinates at different times.

The effect depends on the scale of noncommutativity and Brownian motion parameters.

Potential experimental signatures of spatial noncommutativity are identified.

Abstract

We investigate the classical Brownian motion of a particle in a two-dimensional noncommutative (NC) space. Using the standard NC algebra embodied by the sympletic Weyl-Moyal formalism we find that noncommutativity induces a non-vanishing correlation between both coordinates at different times. The effect stands out as a signature of spatial noncommutativity and thus could offer a way to experimentally detect the phenomena. We further discuss some limiting scenarios and the trade-off between the scale imposed by the NC structure and the parameters of the Brownian motion itself.